A club has 10 members, 5 boys and 5 girls.  Two of the members are chosen at random.  What is the probability that they are both girls?
There are $\binom{10}{2} = 45$ ways to choose two members of the group, and there are $\binom{5}{2} = 10$ ways to choose two girls.  Therefore, the probability that two members chosen at random are girls is $\dfrac{10}{45} = \boxed{\dfrac{2}{9}}$.